The major 6th harmony interval in music is in Φ ratio to the octave. For example, the finger bones are in approximate Φ ratio to each other, and the position of features on the human face is related to Φ. Le Corbusier's The Modular represents a more recent study of the Golden Ratio in the human form. Recall Vitruvian Man, a drawing by Leonardo showing man within the circle and the Golden Ratios in the human body. Φ shows up throughout nature and represents one of the most fundamental numerical constants of the universe. Shamans, priests, and artists throughout the world and across history have understood and applied Φ to ritual, architecture, art, and the crafting of musical instruments and everyday objects. It is called phi, Φ, in honor of Phidias, the architect of the Parthenon, and is approximated by the irrational fraction 0.618034. The Egyptians knew about it and the Greeks learned about it from them. Knowledge of the Golden Section, ratio, or proportion has been known for a very long time. One of the best examples of Sacred Geometry are forms based on the Golden Ratio. So, geometry that refers to the structural unity of nature is a powerful metaphor for the mystery of life, and thus sacred. Structural forms seen at the microscopic level are repeated at other scales, and the laws of fractional symmetry appear to apply throughout. This is a truth that is readily felt by sensitive people, and has been demonstrated by science and mathematics. Our universe is structured in a highly complex yet sublimely ordered manner. This includes the geometry and numerological mysticism of the Pythagoreans and the alchemists, but also the fractal geometry discovered through science. When I refer to Sacred Geometry, I am talking about geometry that is derived from or directly related to the structure of nature. To me, sacred means something that is symbolic of a trancendent truth, and worthy of study, contemplation, and veneration. The Algebraic Derivation of the Golden Ratio The Golden Rectangle as a Rudimentary Fractalĭraw a Golden Rectangle with Compass and Straightedge The Square-Root of 5 and the Golden Rectangle
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